Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Lipid-gramicidin interactions: dynamic structure of the boundary lipid by 2D-ELDOR.

The use of 2D-electron-electron double resonance (2D-ELDOR) for the characterization of the boundary lipid in membrane vesicles of DPPC and gramicidin A' (GA) is reported. We show that 2D-ELDOR, with its enhanced spectral resolution to dynamic structure as compared with continuous-wave electron spin resonance, provides a reliable and useful way of studying lipid-protein interactions. The 2D-ELDOR spectra of the end-chain spin label 16-PC in DPPC/GA vesicles is composed of two components, which are assigned to the bulk lipids (with sharp auto peaks and crosspeaks) and to the boundary lipids (with broad auto peaks). Their distinction is clearest for higher temperatures and higher GA concentrations. The quantitative analysis of these spectra shows relatively faster motions and very low ordering for the end chain of the bulk lipids, whereas the boundary lipids show very high "y-ordering" and slower motions. The y-ordering represents a dynamic bending at the end of the boundary lipid acyl chain, which can then coat the GA molecules. These results are consistent with the previous studies by Ge and Freed (1999) using continuous-wave electron spin resonance, thereby supporting their model for GA aggregation and H(II) phase formation for high GA concentrations. Improved instrumental and simulation methods have been employed.